MATHEMATICS II

So the correct answer is C.

Now, substitute this value of x into any one of the equations to obtain the value y=-53/30. Hence the correct answer is B.

For the point (0, 4) if we insert this point into first inequality we see that

is not true. Also for the point (6, 0) if we insert this point into the third inequality we see that

is not true. Therefore the points (0, 4) and (6, 0) do not belong the constraint set. The corner points for the constraint set are (0, 3), (-4, 0), (0, 0) and (-2/3, 10/3). Hence the correct answer is B.

 for the point (5, 0) we have

for the point (0, -2) we have

for the point (3, -2) we have

Hence the maximum point is 20 and the correct option is D.

we can check which one of them satisfies the inequality with the point (0, 0) which is

Hence the correct answer is E.

For the point (0, -2) if we insert this point into fourth inequality we see that

is not true. Also for the point (6, 0) if we insert this point into the first inequality we see that

is not true. Therefore the points (0, -2) and (6, 0) do not belong the constraint set. The corner points for the constraint set are (0, 3), (3, 0), (0, 0) and (30/7, 6/7). Now, to find the maximum value we need to substitute each corner point to the goal function. Observe that for the point (0, 0) we have

maximum point is 15 and the correct option is A.

for the point (-7, 0) we have

 for the point (0, -4) we have

for the point (-3, -1) we have

Hence the maximum point is 24 and the correct option is C.

is not true. For the point (1, -5) if we insert this point into the second inequality we see that

is not true. For the point (3, 3) if we insert this point into the first inequality we see that

is not true. For the point (4, -2) if we insert this point into the second inequality we see that

is not true. The point (3, -2) satisfies all there inequalities because

Hence the correct answer is B.

So the correct answer is D.

Correct answer is  E .

Correct answer is D  .

Correct answer is B .

Correct answer is A

Correct answer is D

Correct answer is E

Multiply the second  equation by -2   and  add to first equation

The intersection points are 

 The points  (2,0) and (0,4)  do not belong to the constrained set. The corner points of the constraint set are

Correct answer is C

is straight line with  x-axis intercept (3,0), y-axis intercept (0,2). The point (0,0)  statisfies

therefore  (0,0)  belongs to the half plane

Correct answer is B

Correct answer is C

The maximizing point is (6,2) and the maximum value is 54.

Correct answer is D